How does fertilization produce a new horsetail sporophyte?

In the life cycle of horsetails (Equisetum), fertilization is the process that initiates the development of a new sporophyte.1

The process occurs as follows:

• Gamete Production: Horsetails are homosporous, producing spores that grow into independent, green gametophytes. These gametophytes produce male gametes (antherozoids) in antheridia and female gametes (eggs) in archegonia.12
• Fertilization: When moisture is present, the flagellated antherozoids swim to the archegonia to fertilize the egg, forming a zygote.12
• Embryo Development: The zygote undergoes cell division to form an embryo within the archegonium. Specifically, the zygote divides by transverse and longitudinal walls into a group of four cells: the two cells toward the neck of the archegonium give rise to the shoot system, while the inner two produce the foot and root.13
• Maturation: The young sporophyte is nourished by the gametophyte until it develops its own roots and shoots, eventually becoming the mature horsetail plant.41